The indigenous culture of school mathematics in China and the United States: a comparative study of teachers\u27 understanding of constructivism

This study aimed to explore how the indigenous (national) culture of teaching and learning mediates teachers’ understandings of constructivism in China and the U.S. Thirty middle school math teachers who are self-identified with the mathematics teaching reform movement in each country participated in this study (NCTM 2000 Math Standards in the United States or the MOE 2001 Math Standards in China). Both theoretical and empirical methods were adopted for this research. Theoretical analysis led to a new cultural model that helped select appropriate cultural elements for this study. Based on emergence theory, the new model perceives Confucianism and Taoism as the most influential beliefs and values in terms of teaching and learning in China, in contrast with Behaviorism and Individualism in the U.S. This study revealed that the indigenous culture of China and U.S. greatly influenced teachers’ understandings of teaching and learning. Chinese participants tended to advocate Eastern belief that math learning develops through mental struggle, and is facilitated by providing hints, whereas their American counterparts tended to have faith in the Western belief that properly sequenced instruction supplemented by general encouragement of students will lead to learning. However, in some cases teachers’ responses defied the predictions of the cultural model. For instance Chinese and American teachers both tended to opt for the Eastern belief of creating pedagogical balance as opposed to the Western belief in choosing a single well-chosen method. The differences and commonalities between Chinese and American participants’ understandings of learning and teaching are thoroughly explored in this study. The key issue of transportability of recommended pedagogical practices across cultural boundaries is discussed in the Conclusions section

Perturbation theory for evolution of cooperation on networks

Network structure is a mechanism for promoting cooperation in social dilemma games. In the present study, we explore graph surgery, i.e., to slightly perturb the given network, towards a network that better fosters cooperation. To this end, we develop a perturbation theory to assess the change in the propensity of cooperation when we add or remove a single edge to/from the given network. Our perturbation theory is for a previously proposed random-walk-based theory that provides the threshold benefit-to-cost ratio, $(b/c)^*$, which is the value of the benefit-to-cost ratio in the donation game above which the cooperator is more likely to fixate than in a control case, for any finite networks. We find that $(b/c)^*$ decreases when we remove a single edge in a majority of cases and that our perturbation theory captures at a reasonable accuracy which edge removal makes $(b/c)^*$ small to facilitate cooperation. In contrast, $(b/c)^*$ tends to increase when we add an edge, and the perturbation theory is not good at predicting the edge addition that changes $(b/c)^*$ by a large amount. Our perturbation theory significantly reduces the computational complexity for calculating the outcome of graph surgery.Comment: 31 pages, 6 figure

Persistent Kernels for Iterative Memory-bound GPU Applications

Iterative memory-bound solvers commonly occur in HPC codes. Typical GPU implementations have a loop on the host side that invokes the GPU kernel as much as time/algorithm steps there are. The termination of each kernel implicitly acts as the barrier required after advancing the solution every time step. We propose a scheme for running memory-bound iterative GPU kernels: PERsistent KernelS (PERKS). In this scheme the time loop is moved inside a persistent kernel, and device-wide barriers are used for synchronization. We then reduce the traffic to device memory by caching a subset of the output in each time step in registers and shared memory to be used as input for the following time step. PERKS can be generalized to any iterative solver: they are largely independent of the solver's implementation. We explain the design principle of PERKS and demonstrate the effectiveness of PERKS for a wide range of iterative 2D/3D stencil benchmarks (geometric mean speedup of $2.29$x in small domains and $1.53$x in large domains), and a Krylov subspace solver (geometric mean speedup of $4.67$x in smaller SpMV datasets from SuiteSparse and $1.39$x in larger SpMV datasets, for conjugate gradient)

Exploiting Scratchpad Memory for Deep Temporal Blocking: A case study for 2D Jacobian 5-point iterative stencil kernel (j2d5pt)

General Purpose Graphics Processing Units (GPGPU) are used in most of the top systems in HPC. The total capacity of scratchpad memory has increased by more than 40 times in the last decade. However, existing optimizations for stencil computations using temporal blocking have not aggressively exploited the large capacity of scratchpad memory. This work uses the 2D Jacobian 5-point iterative stencil as a case study to investigate the use of large scratchpad memory. Unlike existing research that tiles the domain in a thread block fashion, we tile the domain so that each tile is large enough to utilize all available scratchpad memory on the GPU. Consequently, we process several time steps inside a single tile before offloading the result back to global memory. Our evaluation shows that our performance is comparable to state-of-the-art implementations, yet our implementation is much simpler and does not require auto-generation of code.Comment: This is short paper is published in the 15th workshop on general purpose processing using GPU (GPGPU 2023

Polycyclopentene crystal-decorated carbon nanotubes by convenient large-scale in situ polymerization and their lotus leaf-like superhydrophobic films.

In situ Pd-catalyzed cyclopentene polymerization in the presence of multi-walled carbon nanotubes (MWCNTs) is demonstrated to effectively render, on a large scale, polycyclopentene-crystal-decorated MWCNTs. Controlling the catalyst loading and/or time in the polymerization offers a convenient tuning of the polymer content and the morphology of the decorated MWCNTs. Appealingly, films made of the decorated carbon nanotubes through simple vacuum filtration show the characteristic lotus-leaf-like superhydrophobicity with high water contact angle (>150°), low contact angle hysteresis (<10°), and low water adhesion, while being electrically conductive. This is the first demonstration of the direct fabrication of lotus-leaf-like superhydrophobic films with solution-grown polymer-crystal-decorated carbon nanotube

Comparison Study of Classification Model for Forest Cover Type Prediction

Forest is one of the most important natural resource that correlate to biodiversity, climate, geochemical aspect. Forest cover type is a dominant kind of tree cover in certain area. This study is addressing a multiclass classification problem of forest cover type via supervised learning method. The cartographic feature of forest will be retrieved from dataset of Roosevelt National forest. There exist seven types of trees and fifty-five environmental features in the area. Six machine learning models, K-NN, linearSVC, logisticRegression, GaussianNB, DecisionTree and RandomForest classifier are implemented and compared. K-NN algorithm gains the best prediction accuracy and best overall performance over all the classes.Master of Science in Information Scienc

Perceptions of Teachers, Students and Parents of the Characteristics of Good Teachers: A Cross-Cultural Comparison of China and the United States

Since the 1920\u27s many researchers have conducted studies exploring the qualities of good teachers. However, a limited number of empirical studies have been conducted in the People\u27s Republic of China (hereafter called China). The current study has two objectives. The first one aims to compare a good teacher\u27s characteristics in China and the USA. To achieve this, qualitative data of a good teacher\u27s characteristics were collected in China. The results obtained from China were then compared to those reported in the USA. The second objective was to test whether or not there are differences among teachers\u27, students\u27 and parents\u27 perceptions of a good teacher\u27s characteristics in China. To achieve this, questionnaires were administered, and then statistical analyses were conducted. The qualitative data analyses have revealed four themes about the characteristics of good Chinese teachers: Teacher ethics, professional skills, professional development, and students\u27 test scores. The ANOVAs have found no differences among teachers\u27, students\u27 and parents\u27 perceptions of the qualities of good teachers in China on most of the items. This study helps readers better understand good teachers in a Chinese context and provides a framework for future comparative study between China and the USA regarding the qualities of good teachers

Re-examining Factor Structure of the Attitudinal Items From TIMSS 2003 in Cross-Cultural Study of Mathematics Self-Concept

The aims of this study were to examine the factor structure of the attitudinal questionnaire items from Trends in International Mathematics and Science Study (TIMSS) 2003 and to investigate low- and high-performing students\u27 mathematics self-concept in East Asian societies and in the USA. The participants were 24,119 eighth-graders, 4856 from Japan, 4972 from Hong Kong, 5379 from Taiwan and 8912 from the USA. Exploratory factor analyses (EFAs) were conducted revealing a same factor structure across the four societies. The MANOVA results showed that (1) the US students reported a statistically significant higher mathematics self-concept than students in Hong Kong, Taiwan, or Japan; (2) across the four societies, high-performing students had statistically significant higher self-concept than low-performing students; and (3) the US low-performing students\u27 self-concept was higher than Japanese high-performing students\u27 self-concept. The implications of these findings are discussed

An Infiltrative Approach to Reform Mathematics Teaching:An Analysis of Chinese Middle School Teachers’ Lessons

The newly established mathematics curriculum and teaching standards in the U.S. and many other countries direct mathematics teachers to transform their lesson structure, focus, and activities from the popular teacher directed instruction to student inquiry-oriented teaching. An appropriate understanding about how mathematics teachers implement the above change constitutes an important knowledge base for relevant policy making to mathematics teaching reform. Framed by the constructivist and the situated assumptions about teacher reform, this study examines the changed structural patterns, focuses, and activities of mathematics lessons and the teaching contexts shaping these changes drawing on mathematics lessons that 30 Chinese teachers taught and the interviews with some of them about their lessons. The study found that most of these teachers designed their lessons by infiltrating the ideas and activities envisioned by the reform curriculum standards into their existing teaching structure without undergoing a lesson overhaul transformation. The centralized curriculum standards and materials, contrived teaching organization, and accountability assessment in China impacted importantly on the patterns, focuses, and activities of their lessons designed to reflect their ideas of mathematics teaching reform